What is the ratio of 24 to 32 as a fraction in simplest form with whole numbers in the numerator and denominator
The correct answer and explanation is:
The ratio of 24 to 32 can be written as the fraction 2432\frac{24}{32}. To simplify this ratio, we need to find the greatest common divisor (GCD) of 24 and 32. The GCD is the largest number that divides both 24 and 32 evenly.
Step 1: Find the GCD of 24 and 32
The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 32 are:
1, 2, 4, 8, 16, and 32.
The greatest common divisor is 8, since it is the largest number that appears in both lists of factors.
Step 2: Divide both the numerator and the denominator by the GCD
Now that we know the GCD is 8, we divide both the numerator (24) and the denominator (32) by 8: 2432=24÷832÷8=34\frac{24}{32} = \frac{24 \div 8}{32 \div 8} = \frac{3}{4}
Conclusion:
The ratio of 24 to 32 in its simplest form is 34\frac{3}{4}. This is the fraction representing the ratio with the smallest whole numbers in both the numerator and the denominator.
Why Simplification is Important:
Simplifying ratios is crucial because it makes the relationship between the two numbers easier to understand and compare with other ratios. The simplified form provides the most direct and efficient way to express the ratio, especially in applications where precision and ease of use matter, such as in mathematics, engineering, and everyday life.
By simplifying ratios, one can reduce the complexity and make calculations and comparisons more straightforward. In real-world applications like recipes, measurements, or budget calculations, working with simpler numbers can save time and reduce errors.